ame Date Class Practice A Polygons Name each polygon. 1. 2. 3. 4. 5. 6. Tell whether each polygon appears to be regular or not regular. 7. 8. 9. 10. What is another name for a regular triangle? 11. What is another name for a regular quadrilateral with four right angles? 12. One side of a regular pentagon measures 4 inches. What is the total length of the sides of that pentagon? 13. The total length of the sides of a regular octagon is 24 inches. What is the length of each side?
Practice B Polygons Name each polygon and tell whether it appears to be regular or not regular. 1. 2. 3. 4. 5. 6. 7. The public swimming pool is in the shape of a regular hexagon. Each side of the pool measures 5 feet. What is the distance around the entire pool? 8. In the space below, draw a regular quadrilateral. Now draw one diagonal of that quadrilateral. Describe the two polygons that are formed.
Practice C Polygons Name each polygon and tell whether it appears to be regular or not regular. 1. 2. 3. Explain why each shape is not a polygon. 4. 5. 6. 7. The perimeter of a flower bed designed in the shape of a regular hexagon is 28 1 feet. What is the length of each side of the 2 flower bed? 8. How many diagonals can you draw from one vertex of a regular hexagon? What is the least number of triangles needed to fill a regular hexagon? 9. What is the total number of diagonals that can be drawn in a regular pentagon? Describe the figure formed by the diagonals.
Review for Mastery Polygons A polygon is a closed plane figure formed by three or more line segments. Polygons are named by the number of their sides and angles. Sides and Angles 3 4 5 6 7 Polygon triangle quadrilateral pentagon hexagon heptagon A regular polygon has all congruent sides and angles. Each angle is 90 degrees. Each side is 3 centimeters long. If the angles and the sides are not all congruent, then the polygon is not regular. Name each polygon and tell whether it is regular or not regular. 1. 2. _ To find the angle measures of a regular hexagon, first divide the polygon into triangles by drawing connecting segments from one vertex to all of its nonadjacent vertices. There are 4 triangles. Next, multiply the number of triangles by 180. 4 180 = 720 The sum of the angle measures of a triangle is 180. Divide the product by 6, the number of sides, to find the measure of each angle. 720 = 120 All of the angles of a regular polygon are congruent. 6 Each angle is 120. Find the angle measure of each regular polygon. 3. regular quadrilateral 4. regular pentagon
Challenge Sign Language Traffic signs are symbols used to convey information. In the United States, certain shapes are used only for certain traffic signs. As a result, you can often understand the message of a traffic sign simply by classifying its geometric shape. Tell whether each traffic sign below is a polygon. If it is, name the polygon that best describes its shape, and tell whether it appears to be regular or not regular. 1. 2. 3. 4. 5. 6. 7. 8. 9.
Problem Solving Polygons Write the correct answer. 1. Name each polygon in this figure. 2. How could you use the sum of the angles inside a triangle to find the sum of the angles inside a heptagon? 4. In the space below, draw a rectangle and a parallelogram with side lengths congruent to the rectangle s. Now draw the diagonals for each of those polygons. What new polygons are formed by the diagonals in each quadrilateral? 3. How could you use the sum of the angles inside a triangle to find the sum of the angles inside a decagon? 5. In Exercise 4, what is true of the diagonals in the rectangle that isn t true of the diagonals of the parallelogram? Circle the letter of the correct answer. 6. The perimeter of a regular hexagon is 13 1 inches. What is the length of 2 each side? A 2 7 10 inches C 3 3 4 inches B 2 1 4 inches D 1 11 16 inches 7. Which of the following statements is sometimes false? F A plane figure is a polygon. G Each side of a polygon intersects exactly two other sides. H A polygon is a closed figure. J A polygon has straight sides.
Reading Strategies Focus on Vocabulary A polygon is a closed, plane figure formed by three or more line segments. In a regular polygon, the sides are of equal length and all angle measures are the same. Regular Polygon Not Regular Polygon The prefix of a polygon is a clue that can help you understand the number of sides and angles it has. Tri- means three Quad- means four A triple play means three outs all at once. A triangle has three sides and three angles. Quadruplets are four babies born at the same time. A quadrilateral has four sides and four angles. This table helps you organize polygons by their sides and angles. Polygon Number of Sides Number of Angles Triangle 3 sides 3 angles Quadrilateral 4 sides 4 angles Pentagon 5 sides 5 angles Hexagon 6 sides 6 angles Octagon 8 sides 8 angles Write the name of each polygon. Also write whether the polygon is regular or not regular. 1. 2. 3. 4. _
Puzzles, Twisters & Teasers Seeing is Believing There are three correct answers for each problem. Circle the single incorrect statement. The letters next to the incorrect statements will provide the solution to the riddle when they are matched with their problem numbers on the blanks below. 1. 2. T has 6 angles U has no sides F is an octagon E is an oval N is an irregular polygon A is not a quadrilateral A has 6 sides Y is a polygon 3. 4. L has 3 sides O is an octagon K is an isosceles triangle A sum of the interior angles is 720 P is not a polygon G can be divided into 6 triangles D sum of interior angles equals 180 S has 8 angles 5. 6. P has 4 right angles K is a polygon L is not a quadrilateral S has 4 congruent sides H has 4 sides N is a trapezoid W sum of interior angles equals 360 T is a quadrilateral 7. 8. O sum of interior angles equal 560 U has 5 sides J is a square M is a regular polygon E can be divided into 3 triangles F sum of the interior angles is 360 A has 5 angles What kind of glasses do spies use? C sides are not congruent 6 3 2 1 7 8 4 5 6
Answers CODE 60807 LESSON Practice A 1. triangle 2. hexagon 3. octagon 4. quadrilateral 5. pentagon 6. quadrilateral 7. regular 8. not regular 9. regular 10. an equilateral triangle 11. a square 12. 20 inches 13. 3 inches Practice B 1. triangle; not regular 2. hexagon; regular 3. octagon; regular 4. quadrilateral; regular 5. pentagon; not regular 6. quadrilateral; not regular 7. 30 feet 8. They are both triangles. Practice C 1. hexagon; not regular 2. octagon; regular 3. quadrilateral; not regular 4. It is not a closed figure. 5. One of its sides is not a line segment. 6. It does not have any line segments. 7. 4 3 4 feet 8. 3 diagonals, 4 triangles 9. 5 diagonals, a 5-cornered star Review for Mastery 1. quadrilateral, regular 2. quadrilateral, not regular 3. 90 4. 108 Challenge 1. yes, octagon, regular 2. not a polygon 3. yes, triangle, regular 4. yes, pentagon, not regular 5. yes, quadrilateral, not regular 6. not a polygon 7. yes, trapezoid, not regular 8. yes, quadrilateral, regular 9. yes, triangle, not regular Problem Solving 1. 1, 2, 4, 5, and 6 are triangles; 3 is a parallelogram; 7 is a square (some students may name the entire figure a square) 2. Five triangles are needed to fill a heptagon; 5 180 = 900. So, the sum of the angles inside a heptagon is 900. 3. Eight triangles are needed to fill a decagon; 8 180 = 1,440. So, the sum of the angles inside a decagon is 1,440. 4.
triangles 5. The diagonals in the rectangle are congruent. 6. B 7. F Reading Strategies 1. pentagon, regular 2. pentagon, not regular 3. quadrilateral, not regular 4. octagon, regular Puzzles, Twisters & Teasers 1. F 2. Y 3. P 4. A 5. L 6. S 7. O 8. C S P Y F O C A L S